Simultaneous parametric estimation of shape and impedance of a scattering surface using a multi-frequency fast indirect boundary element method

Characterization of rough surface properties, such as surface shape or surface impedance, is relevant in many applications. Previous work has been done for characterizing these two aspects separately. This paper proposes a framework for characterizing rough surfaces of finite size in terms of their roughness shape and surface impedance in a single setup. The surface properties are estimated indirectly using a superposition of spatial sinusoidal components for the surface shape and a porous material model for the surface impedance. A fast multipole indirect boundary element method is employed to model the acoustic scattering problem. With the modeling flexibility from the indirect formulation, the target geometry can be simplified as a thin shell representation, which significantly improves computational efficiency. A subtraction method is proposed to mitigate the modeling error of this representation and enable the use of low driving frequencies (e.g. acoustic wavelength is comparable to or larger than the roughness scale) in the characterization. Considering the modeling accuracy of surface shape representation, a discretization criterion concerning both acoustic and spatial aspects is defined. The inverse problem is solved by means of a general-purpose optimizer, minimizing the difference between the simulated and reference acoustic field at multiple driving frequencies. Various numerical examples show that by using reference data with sufficient quality, the proposed framework can retrieve the surface shape and impedance separately, and also simultaneously.